N O T I C E 

THIS DOCUMENT HAS BEEN REPRODUCED FROM 

MICROFICHE. ALTHOUGH IT IS RECOGNIZED THAT 

CERTAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RELEASED 

IN THE INTEREST OF MAKING AVAILABLE AS MUCH 

INFORMATION AS POSSIBLE 
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Augu:;t 1984

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NASA Contractor Report 174946

Time Dependency of Strainrange

Partitioning Life Relationships

( N ASA-C;E;-174946) TIME DEPENHENCY OF N86-13755 SUAINRANGE P APII7ICNING LIFE FELATIONSHIPS

Final Beport (Casc Western Reserve Univ.)

64 p HC A04/nk A01 CSCL 20K Uncles

G3/39 04947

Sreeramesh Kalluri and S.S. Manson

Case Western Reserve University

Cleveland, Ohio

Prepared for the

Lewis Research Center

Under Contract NAG 3-337

'i Aerorj&A' lr^

,;^,, ^^ Aamn^^>IraDun
TIME-DEPENDENCY OF SRP LIFE RELATIONSHIPS

INTRODUCTION

Strainrange Partitioning (SRP) is a method developed by Manson. HaIford

and Hirschberg [1) to determine the cyclic lives of engineering materials used in

components subjected to high temperature low cycle fatigue (HTLCF) . Conventional SRP recognizes inelastic strainrange as the primary variable governing cyclic life and distinguishes between four different types of strainranges (PP, PC.

CC and CP) . These generic strainranges constitute the basic waveforms in

which creep can be combined with plasticity. However, within each waveform of

loading involving creep strain, secondary variables such as creep rate and

exposure-time can influence cyclic life in HTLCF. These two secondary variables

are not independent of each other. Creep rate is inversely related to the exposure time for failure. Although account is taken in a secondary manner by using modifications based on tensile test ductility and creep test ductility the

characterizing SRP relationships are obtained experimentally without regard for the

time involved in any one test.

Long-time duration creep-fatigue tests are not only expensive to conduct in

the laboratory but it is also difficult to maintain all the controlling parameters

(such as temperature. load or strain. etc. ) without fluctuations during the entire

life time of such a test. Hence most of the tests conducted in the laboratory

tend to be short time duration tests with the failure time of the order of a few

hours to a few hundred hours. However, in practice jet engine hot section

components, and nuclear reactor components which operate at high temperatures, must be designed for several thousand hours and even hundreds of

1

4
t thousands of hours. Therefore, when creep-fatigue data that are generated at

short times in the laboratory are extrapolated to the long time practical applicaons. the time dependency of life relationships should be properly taken into

consideration.

At high temperatures environmental effects. such as oxidation, corrosion, and

metallurgical instabilities such as precipitation of new phases and dissolution of

the existing phases influence the cyclic life of an engineering component. All of

the above phenomena are dependent upon time, and are capable of modifying

the mechanical properties (e. g. embrittlement of nickel alloys due to precipitation

of sigma phase with time) and the creep response of a material as the time

progresses. Since all of these time dependent factors influence the cyclic life of

a component. it is very important to consider the time dependency (or the effect

of creep rate) of the Strainrange Partitioning life relationships. The goal of this

study was to establish quantitatively the effect of exposure time within the CP type

of strainrange.

A series of isothermal CP tests with varying exposure times were conducted

on 316 SS at 1300°F and 1500°F. Post failure fractography and metallography

studies were conducted to establish the effect of the failure time (or creep

rate) . The experimental technique used, the results of the experiments and the

metallurgical studies together with the recently proposed Steady State Creep Rate

Modified CP life relationship and the Failure Time Modified CP life relationship

are presented in this report.

1

A

7=^)

2

w
ri

P r ALTERNATE METHODS OF TREATING TIME EFFECTS 14

IN HIGH TEMPERATURE LOW CYCLE FATIGUE

2) Frequency Modified Lft Equation

The Frequency Modified Life relationship was proposed by Coffin [6) to account for time effects associated with frequency variation during constant strain

rate tests at high temperatures. For this equation which is given below. cyclic

life, N f was modified by using frequency, v associated with that life.

k^

AE = C 2 IN f

vk-1 1-B t E Nf 'B v ) (1)

AE = Total strainrange

N f = Failure life

v = frequency

C 2 , k -8, A' . R' and k are all temperature dependent constants which are

evaluated by c')nducting strain rate controlled tests at various frequencies. In

the above equation the effect of wave form of loading on cyclic life was not considered. Further modification of the Frequency Modified Life equation such as

Frequency Separation etc.. were later proposed in Ref. [6) to include this effect.

^. Ductilit Normalized SRP Life Relationships

The Ductility Normalized SRP life relationships are a set of universalized SRP

life relationships first proposed by Manson (7), and later modified by Halford,

Saltsman and Hirschberg [2). These life relationships are based on the creep

and plastic ductilities which the material exhibits in the environment of interest.

The ductility corresponding to the teneile ha'f of the generic loop is used in the

3
ON-SRP life relationships. Plastic ductility DP is used for predicting the lives of

PP and PC cycles, whereas creep ductility. D c is used for predicting the lives of

CP and CC cycles. Ductility-Normalized SRP life relationships as proposed by

Halford. Saltsman and Hirschberg are.

2eE I-1.67

NPP =

O 

(2)

P

4eE 1

-1 67

NPC = D PC J

(3)

P

NCC = Dc f4AE CC l

-1.67

(4)

NCP = D

C (5e E CP 1 1.57 (transgranular) ( 5a)

NCP = DC (l0e ECP J 

-1.67 ( lntergranular) ( 5b)

The Ductility Normalized SRP life relationships can be used in two ways:

( i) Using DN-,SRP litg relationships only:

In this case, the effect of exposure time is taken into account by using the

ductility DC . or DP . corresponding to the failure time of the test. These ductility values are used to evaluate the cyclic lives using Eqs. (2)-(5). The variation of ductility with rupture time is obtained from static creep rupture tests in

the environment of interest.

' yv.

4
^ 1 . a^..^ 1

`►aan ^^^s:Y^w.'+'^ A-. -.Fiat ^... .Qy..i -:_. _y ,:.. _

(ii) in QN-$RP t relationships in coniunction with experimentally obtain ed

I_hgrt-time ,SRP I_fg relationships:

SRP life relationships can easily be generated in the laboratory for short time

duration tests. These life relationships can be extrapolated to long time durations using the Ductility-Normalized life relationships. At a given inelastic strainrange. the following equation can be obtained from Eqs. (2)-(5):

8

Vshort = 

I

D

1 (6)

long short

where the exponent a is obtained from the appropriate life relation in the short

time duration tests.

g) CritiQue

The Frequency Modified Life equation utilizes continuous cycling data, generated at various frequencies as the baseline data to evaluate the constants of

Eq. (1) . In doing so, the nature of the strainrange (or waveform of loading)

is also varied simultaneously ( from PP to a combination involving both PP and

CC) . The effects of waveform of loading and frequency of loading on cyclic life

are combined in Eq. ( 1) . Thus the Frequency Modified Life relationship consists of a combination of two different types of strains (PP and CC) , together

with the time effects of CC. As a result, it should not be applied to determine

the cyclic life when frequency is varied within strainranges such as CP and PC.

The life predictions by DN-SRP life relationships are generally within a factor

of 3 of the observed lives. However. ON-SRP life relationships somF;times tend

to predict values that are not completely in agreement with the trend observed in

the experimental data, as later illustrated in this report.

5
In view of the above limitations of the previous methods. there is a necessity

for another technique, which can quantitatively predict the effect of frequency

within different types of waveforms in a distinct manner without mixing the effects

of frequency and different types of strainranges on the cyclic life.

THE EFFECT OF FREQUENCY ON CYCLIC LIFE

WITHIN A GIVEN WAVEFORM OF LOADING

The Strainrange Partitioning method developed to date accounts for the variation of cyclic life due to different types of waveforms. This is accomplished by

considering the following four types of strainranges and the associated life relationships:

NPP = A [6,E PP 

j 

C' )

NCP = B (DECP )a (7b)

NPC C (DEpc l y

(70

Ncc = D (AECC) i5 (7d)

where

AEA = generic strainrange

Ni i = cyclic life associated with the generic strainrange

i = p ( plasticity) . c ( creep)

= p.c

The damage associated with any hysteresis loop containing more than one

generic strain range is calculated using the Interaction Damage rule (7) given

6

=' 0,0 r''
below.

NPp t Ncc t IN or NcP 

1 

= N (8)

PP cc pc cp f

where

AE

_ ^.i i = p.c F.

.

. 1 eEin j = p . c

Ni i = cyclic life associated with AE i. considering A E; i = AEin

( Eqs. 7) .

N f = Predicted cyclic life of the hysteresis loop.

The effect of frequency within a given waveform of loading can be accomplished by modifying Eqs. (7) . Hence the effect of waveform of loading and

the effect of frequency within each waveform are obtained in a distinct manner

without changing the nature of strainrange and frequency at the same time.

In the following sections of this report. the effect of frequency within the CP

type of strainrange is presented.

(a) Tensile Strain Hold and Stress Hold Tests

CP type of loading is encountered in engineering practice at high temperatures whenever tensile creep is reversed by compressive plasticity. Typical examples of CP type of loading are strain-hold and Stress-hold tests in tension.

Figure 1 shows a strain-hold hysteresis loop abcdea . The vertical line cd indicates tensile strain hold at maximum tensile strain. The amount of elastic strain

converted into creep strain is indicated by c'e during the tensile strain hold.

The same amount of creep strain can also be introduced by holding the stress at

its maximum value. i. e. a stress-hold at the maximum tensile stress along horizontal line cd ' ; however, the time required to complete loop abed 'ea ( stress

hold at maximum tensile stress) is much smaller than the time required to

7

^ ter

^
Stress

e d'

' r ^ E

^

' d

,

rain

Lein - be

A[pp be'

QEcp • Cle

1parision of a Tensile Strain Hold Test

.h a Tensile Stress Hold Test.
w^ r1#

complete loop abcdea ( strain hold) at maximum tensile strain. This is due to

the fact that in loop abcd'ea (stress hold) , the entire amount Of creep strain is

introduced at the maximum tensile stress, whereas in loop abcdea (strain-hold),

creep is introduced at progressively decreasing stress levels, the maximum being

the, same as that of loop abcdea . The cyclic lives of the above loops can

differ substantially due to several reasons such as environmental effects, metallurgical instabilities, etc. Hence it is necessary to develop CP life relationships

to account for different exposure times (or creep rates) .

S'P TESTS WITH VARYING EXPOSURE TIMES

The effect of creep rate (or exposure time) on CP cyclic life was established

by conducting a series of uniaxial isothermal tensile stress hold tests. A

schematic hysteresis loop of a CP test with constant creep strain is illustrated in

Figure 2. The stabilized hysteresis loop is given by BCDEFGH . In tension. first

I`

a required amount of creep strain (ADC'R ) was imposed at a desired stress level

(P ) and the remaining inelastic strain in tension was imposed by rapidly in- CR

creasing the load from G to H to induce plasticity. The load was reversed at

H. and the specimen was rapidly loaded in compression to D. to induce plasticity. The load was reversed again at D . and the specimen was loaded in tension up to the creeping stress level. This loop was repeated until failure.

Varying exposure times were achieved by introducing creep at different stress levels. Experimental details are presented in a more elaborate manner in Ref. (3).

In all of the tests conducted the ratio of total creep strain to total inelastic

strain was maintained at 0.6. At a given inelastic strainrange the total creep

strain was maintained at a constant value. ( Hence these tests are also referred

to as constant creep strain CP tests. ) A general purpose computer program

9
CONCP. BAS was developed in BASIC to conduct these tests. The flowchart, listing of the CONCP. BAS program and sample data input sheet for CONCP. BAS

program are presented in Appendix A. Axial stress and the axial inelastic strainrange were obtained fro..i the applied load and diametral displacement using the

equations given in Ref. (5).

The total inelastic strainrange of the constant creep strain CP test hysteresis

loop was partitioned into generic strainranges CP and PP, considering only the

steady state creep strain occurring during the tensile-stress hold as creep strain.

The generic CP life was obtained using the Interaction Damage Rule. Eq. (8) .

EXPERIMENTAL RESULTS

a) PP I&f tests

PP tests were conducted on 316 stainless steel at 1300°F and 1500 • F to establish the PP life relationships at these temperatures These data are shown in

Tables I and II for temperatures 1300 ° F and 1500 ° F , respectively. The

corresponding life relationships are plotted in Figures 3( a) and 3( b) .

b) .eP tests with v rin ex2osur time

Uniaxial CP tests with constant creep strain (CONCP. BAS) were conducted at

1300°F (using tubular specimens) and at 1500°F (using sold specimens) on

316 stainless steel. These data are shown in Tables III and IV for 1300°F and

1500°F, respectively. It is clear from the data with the exception of one datum

at 1300°F that at a given temperature the cyclic life decreases as the exposure

time increases (or as the creep rate decreases) .

10
TABLE I

PP LIFE RELATIONSHIP RESULTS FOR 316 SS AT 1300'F

(F = 1)

PP

Specimen M AC in N f

PP

BYY-148 0.03600 24

BYY-4 0.02140 50

BYY-173 0.01900 207

BYY-232 0.00630 1408

BYv-21 0.00436 553

BYY-22 0.00136 10170

TABLE II

^l

PP LIFE RELATIONSHIP EXPERIMENTS FOR 316 SS AT 1500°F

(F = 1)

PP

--------------

Specimen 

-------------------

#

--- ------------- ---

------ --

Af. .

in

--_-- ------

^JI

+

Y

BY-86

--- --- - --------

0.03058

--------- ------- --

138

BY-41 0.02010 250

BY-77 0.01996 309

BY-64 0.01189 628

11
10 

10"

Ac

vo

10"

10' S

3

S

!e 1

10

e 

OPP

10"

M

PP

(a) 316 SS at 1300°F.

,,,o

M

DP

(b) 316 SS at 1500°F.

Fig. 3. PP life Relationships.

12

D.-
TABLE III

RESULTS OF CP TESTS WITH VARYING

EXPOSURE TIMES AT 1300-OF

Af = 0.02

PP 

n 

= 1-Fcp

Specimen N FCP 0C (KSI) t, (hr) Es

(In /ir ?ruin)

N f NCP

BYY-218 0.433 36.0 10.1 0.0006062 69 53

BYY-235 0.418 34.0 12.0 0.0004224 52 33

BYY-187 0.417 32.0 27.3 0.0001638 56 37

BYY-239 0.400 30.0 142.3 0.0000431 45 26

TABLE IV

RESULTS OF CP TESTS PITH VARYING

EXPOSURE TIMES AT 1500 OF

F = 1-F

PP Cp

Specimen N &tin %P 0C t

E33 N NCp

(KS) (hr) ( / )

BY-66 0.01 0.419 19.0 7.95 0.001796 215 105

BY-89 0.01 0.222 10.5 169.80 0.000026 124 31

BY-87 0.02 0.543 21.0 3.50 0.004024 94 60

BY-32 0.02 0.458 19.0 4.93 0.002067 80 43

BY-75 0.02 0.364 15.0 21.44 0.000259 58 24

BY-34 0.02 0.315 11.0 95.60 0.000034 46 16

BY-96 0.03 0.565 21.0 2.22 0.003065 29 18

BY-76 0.03 0.335 11.0 101.10 0.000034 22 8

13

1
N-.II

C) Monotonic isothermal creep tests:

a

A series of isothermal monotonic creep tests were conducted on solid specimens of 316 stainless steel at 1500°F. The results of these experiments were

a

utilized in predicting the cyclic lives of CP tests with constant creep strain using

the Ductility-Normalized life relationships (2). The results of these experiments

are tabulated in Table V. The variation of creep ductility, 0 . with the time at

1500°F for 316 stainless steel is shown in Figure 4. The variation of ductility

with rupture time is given by:

D = 2. 395 (tr ) -0. 14 (g)

ANALYSIS OF CP DATA WITH VARYING EXPOSURE TIMES

(I) The raw data of CP tests with constant creep strain, conducted at

1500°F were analyzed using three different types of equations. All the eight data

points were used in generating the life relationships_

a) Conventional Manson-COffin type Qf equation:

Q NCp = P { l

AECP J

where

Ae cp = generic CP strainrange

Ncp = generic CP cyclic life

P and Q are material constants

This equation relates the primary variable, i.e. the generic CP strainrange.

to the generic CP cyclic life. It does not, however, account for time effects

(10)

0

14
101

10 0

DC

10

3

t r (hr'

Fig. 4. Creep-Ductility vs. Rupture Time for 316 SS

at 1500° F.

15
7. i

TABLE V

RESULTS OF CREEP-RUPTURE EXPERIMENTS

ON 316 STAINLESS STEEL AT 1500°F

Specimen M o

(K61)

f

(9r) RA % D - In l l RA

BY-78 19.0 1.7 87.5 2.075

BY-61 15.0 8.4 86.3 1.987

BY-95 11.0 61.0 74.9 1.382

BY-74 9.0 154.7 66.4 1.090

BY-62 7.0 784.2 81.8 0.963

TABLE VI

LIFE PREDICTIONS OF CP TESTS WITH VARYING

EXPOSURE TIMES BY CONVENTIONAL SRP

Specimen 0 Ncp pied Ncp obs N pied N/ obs

BY-88 85 105 140 215

BY-89 65 31 230 124

BY-87 26 80 44 94

BY-32 26 43 51 80

BY-75 26 24 81 58

BY-34 26 16 68 46

BY-96 15 18 24 29

BY-76 15 8 37 22

V

16

J
77171^- _rOT

that can arise within the CP waveform of loading. An equation of the Manson-

' Coffin type ( Eq. (10)) was fitted to the eight data points using linear regression

analysis. The resulting CP life relationship is as follows:

( 1 . 329 Ncp = 0. 1-'42 lAecp 1 (108)

This equation is plotted in Figure 5(a) . It is obvious from the scatter that

the above equation simply averages the diverse behavior of the data. Equation

( 10a) was used to predict the Ncp and N f values corresponding to the strain

ranges of the actual data points. These results are shown in Figures 5(b) and

5(c) . respectively. The conventional Manson-Coffin equation does not take into

consideration the effect of secondary variables such as steady state creep rate

(or failure time) within the CP waveform of loading. Hence Eq. (10a) predicts

the same cyclic life at a given CP strainrange although the creep rates ( hence.

failure times) are entirely different. Also. the trend of the back-calculated N^

lives is completely opposite to the experimentally observed trend. The predicted

N lives were increasing with an increase in the exposure time. This can again

be attributed to the lack of consideration of the exposure times. However. the

predictions of conventional Strainrange Partitioning CP life equation were in most

cases within a factor of 2. These results are presented in Table VI.

b) Steadv t t Creeo Rate Modifie CP Life RelationshiR

Steady state creep rate depends on the temperature and applied stress.

Since creep rate was shown earlier to influence the failure time. it is appropriate

to incorporate it into the CP life relationship. The resulting life relationship is

called the Steady State Creep Rate (SSCR) Modified CP Life Relationship.

17
10 1

02 101 104 105 im

N

cp

.offin equation type of CP Life Relationship

F for 316 SS.

factors of _?

1.5 on late

f

10 1

0

2

101

10100 101 101

M

^t CP 1RLD t•RLD

(b). N cp (c). Nf

Fig. 5. Comparision of Observed and Predicted Cyclic lives

for CP testa with varying exposure times. Life

Predictions based on Manson-Coffin equation type

of CP Life Relationship.

,8
. NCP = A IAECPJa LESS1^ (I 1a)

A , ac. 0 are material constants: ESS is the steady state creep rate at a given

temperature and creep stress. The constants A , a! and A were determined for

the data presented in Table IV using multiple regression analysis. The details of

multiple regression analysis are presented in appendix B of this report. The

resulting equation is as follows:

NCP 

= 0. 6461 ( 

AECP 

1 -1.460 f E

ss 1 0. 2557 11 b)(

Defining Steady State Creep Rate Modified CP generic life N' CP as.

N

N'CP = CP (I1c)

r1 0. 2557

l E SS J

we get N' CP = 0. 6461 1 AE CP -1.460 Equation (11c) is plotted in Figure

6(a) . The NcP and N f values corresponding to AE CP and Ess of the actual

data points were predicted from Eq. (11b) . Comparison of observed vs.

predicted cyclic life is tabulated in Table VII. These results are also presented

in Figures 6(b) and 6(c) .

19
J

I Y - 1

102 M

103 104 10S

c

N cp 0.2557

too

Creep Rate modified CP Life Relationship

Dr 316 SS.

Fig. 6.

.,

I

10 1031 ion"

101 102

M N=

P ARID t'RLD

(b) . N cp (c) . Nf

Comparision of observed and Predicted Cyclic lives

for CP tests with varying exposure times. Life

Predictions Lased on Steady State Creep Rate

modified CP Life Rela-i„nship.

20
TABLE VII

LIFE PREDICTIONS OF CP TESTS WITH VARYING EXPOSURE TIMES

BY STEADY-STATE CREEP RATE MODIFIED CP LIFE EQUATION

Specimen 8 Ncp prod Ncp obs N prod N obs

BY-66 106 105 215 215

BY-80 36 31 140 124

BY-87 47 60 75 94

BY-32 40 43 74 80

BY-75 23 24 55 58

BY-34 14 16 40 46

BY-96 24 18 37 29

BY-76 7 8 19 22

TABLE VIII

LIFE PREDICTIONS OF CP TESTS WITH VARYING EXPOSURE TIMES

BY FAILURE TIME MODIFIED CP LIFE EQUATION

Specimen 0 Ncp prod Ncp obs Ni pred Ni obs

BY-66 103 105 210 215

BY-89 37 31 144 124

BY-87 44 60 7, 94 1

BY-32 39 43 72 80

BY-75 24 24 57 58

BY-34 14 16 40 46

BY-96 26 18 40 29

BY-76 7 8 19 22

4

21
g) FailurQ Time Modifie _ P Life Relationship

This is very similar to the SSCR Modified CP life relationship except that in

this case steady state creep rate is replaced by time to failure of the specimen.

NcP = B L,&Ecp ]

'Y (t f 1 6

( 12a)

where

6 . Y, 6 are material constants

t is the time to failure of the specimen

Again. as in the case of SSCR Modified CP relationship. constants B . 'Y and

8 were determined by multiple regression analysis for the data presented in Table

IV. The resulting Failure Time (FT) Modified CP life equation is as follows:

NcP = 0. 1127 1A Ccp 1 -1 . 631 r tf 

1

-0. 3317 ( 12b)

Failure Time modified CP cyclic life is given by.

IV

N

cP = —

cP = 0. 1127 1 

cP

1

J

AE -1.631 ( 12c)

0.331 7 l 1tf -

This equation is plotted in Figure 7(a) together with the data points. The

observed and predicted cyclic lives are tabulated in Table VIII. These results are

also shown in Figures 7(b) and 7(c) .

The SSCR Modified CP life relation and the FT Modified CP life relation are

not only able to predict the cyclic lives within a factor of 1.5 as compared to

conventional SRP life reli tionship which predicted the lives within a factor of 2.

but their predictions show a trend that is consistent with the experimentally observed behavior. This establishes the fact that there is a time effect within the

22
30

atcv

lo'

lo'

^j

_f

11

—3 101

10T

'o.$

11

M

rposs

I^ 101

1 100

..0

MCF t ^

f

7T7

(a). Failure Time modified CP Life Relationship

at 1500° F for 316 SS.

}

M M

ro VUED ( "=

(b) . N cp (c) . Nf

Fig. 7. Comparision s-)f Observed and Predicted Cyclic lives

for CP tests with varying exposure times. Life

Predicti.c,r,s Teased on Failure Time modified CP

Life Relationship.

23

i

4
CP waveform of loading and that when it is properly accounted for, the predi%-

tions can be improved.

ii) Frequen^v Modifie Lif@ Equation redictions.

Several strain rate controlled continuous cycling tests were conducted at different frequencies (thus generating varying exposure times) on 316 stainless

steel at 1500 °F. The results of these tests are given in Table IX. The plastic

line of the Frequency Modified Life equation is generated using multiple regression analysis.

The resulting Frequency Modified Life Equation is as follows:

N = 2.9737 (pEinI-1. 1709 V 0. 1412 (13a)

Frequency Modified Life

Nf ­6—,7T, -2 = 2. 9737 (pE in l -1.1709 ( 13b) V t )

This equation is plotted in Figure 8(a) together with the data points.

Equation ( 13b) is used to predict the failure lives of the CP tests with varying exposure times at 1500°F. These results are tabulated in Table X and

shown in Figure 8(b) . All the predicted lives are overestimated by at least a

factor of 2. with many points showing a discrepancy of more than a factor of 3.

This is due to the fact that Frequency Modified Lite equation models a mixture of

PP and CC strainranges with the frequency variation superimposed on the strainranges. Hence it cannot distinctly account for the frequency variation within the

CP strainrange. For our tests the predictions were unconservative. the overprediction being as high as a factor of 5. Even higher factors of unconserva24

i

^i
TABLE IX

RESULTS OF CONSTANT STRAIN RATE EXPERIMENTS

ON 316 SS AT 1500°F

Specimen No. Atin Frequency NI

( cpm)

B"y '5' 0.06741 0.01 37

' B^4 0.03287 0.02 105

BY24 0,0294 0. 1 161

BY30 0.00892 1 822

BY42 0.00965 0.1 484

TABLE X

LIFE PREDICTIONS OF CP TESTS WITH VARYING EXPOSURE TIMES

BY FREQUENCY MODIFIED LIFE EQUATION

Specimen ( N f ) prod ( N I ) obs

BY 66 583 215

BY 89 350 124

BY 87 259 94

BY 32 241 80

BY 75 187 58

BY 34 146 46

BY 96 145 29

BY 76 81 22

25
ion

10

10-

10'

ontrolled

cling tests

103

102

(NI)obs

10

t 1

3

N

Nf

t

7 R"

Fig. 8(a). Plastic Line of the Frequency Modified Life

Equation. 316 SS at 1500° F.

(011)OrO4

Fig. 8(b). Comparision of Observed and Predicted Cvclic

lives for CP tests with varying exposure times.

Life Predictions based on the Frequency Modified

Life Relationship. 316 SS at 1500° F,

26

t
tiveness can be expected in other cases.

The SSCR Modified CP life relationship and the FT Modified CP life relations ship account for the frequency effect within the CP strainrange. Hence they are

able to predict the results within a factor of 1.5.

iii) Ductility Normalized _QP Life Relationship Predictions

The creep ductility corresponding to the failure time of the constant creep

strain CP test was evaluated from Eq. (9) . These values were then used in

conjunction with Eq. (5b) to predict the Ncp values. N f predictions were obtained from these Ncp predictions using the Interaction Damage rule. These

results are tabulated in Table XI. A plot of observed vs. predicted cyclic lives

is shown in Figs. 9(a) and 9(b) . In general, the life predictions are within a

factor of 2. Although Ncp predictions follow the same trend with respect to exposure time as the experimentally observed data, the quantitative correlation is

not as good as for the FT Modified CP life equation.

RESULTS OF FRACTOGRAPHY AND METALLOGRAPHY

Post-failure fractographic and metallographic investigations were conducted on

four specimens of constant creep strain CF tests. Two hollow specimens at

1300°F and two solid specimens at 1500°F were selected for these investigations. The goal was to determine any micromechanistic differences between a

high creep rate CP test and a low creep rate CP test 0. e. differences in the

fracture modes, oxide layer formations and metallurgical aspects, etc.) . The

reduction in the CP generic cyclic life as the creep rate decreases can be explained using the results of fractographic and metallographic investigations.

27
101 101

ta.

101

N

=Olf

101 101

100

101 I1

101

N

'PORE

100

10 0

N

t t•NID

(b) . N f

101 101

N

FRU

(a). 

Ncp

I (±)

TABLE XI

LIFE PREDICTIONS OF CP TESTS WITH VARYING EXPOSURE TIMES

BY DN-SRP LIFE EQUATIONS

Spec. No. 66 C tl 0 Ncp prod Ncp obs N/ prod N obs

BY-66 0.01 7.95 1.792 83 105 174 215

BY-89 0.01 169.80 1.167 54 31 198 124

BY-8 7 0.02 3.50 2.010 29 60 49 94

BY-32 0.02 4.93 1.196 28 43 54 80

BY-75 0.02 21.44 1.559 22 24 53 58

BY-34 0.02 95.60 1.265 18 16 50 46

BY-96 0.03 2.22 2.142 16 18 26 29

BY-76 0.03 101.10 1.255 9 8 23 22

Fig. 9. Comparision of Observed and Predicted Cyclic lives

for CP tests with varying exposure times. Life

Predictions based on DN-SRP CP Life Relationship.

28

f^
Fracture surface in a CP test resembles closely the monotonic creep fracture. Fracture occurs mainly due to the separation of grain boundaries. Grain

boundary slip bands and groupings of slip bands reveal the cyclic fatigue character of CP fracture. They form from internal initiation sites very much like striations are formed from external initiation sites. These features which separate intergranular CP fatigue cracking from monotonic fracture are called 'strians' )15).

a) Fracture surface toaography (high cree rate y^. !4w Creep rate CP test)

The differences in the fracture surfaces of a high creep rate (short time

duration) and a low creep rate (long time duration) constant creep strain CP

tests are schematically illustrated in Fig. 10. Though both high and low creep

rate tests are characterized by intergranular fracture, the severity of intergranular

fracture. microvoid formation and oxidation are different in these two cases.

The salient features of the fracture surfaces of a high creep rate and low

creep rate constant creep strain CP tests are as follows:

high creep rate law creep rate

(a) (b)

Regions fractured by intergranular cracking

® Regions fractured in a ductile wanner

Fig. 10. Schematic Illustration of fracture surface

appearances in (a) high creep rate and

(b) low creep rate constant cree p strain

CP tests.

29
Feature Fast creep rate Slow creep rate

1) Number of Large number A single dominant

crack initiation sites crack with fpw iniat the surface of tiation sites

the specimen

2) Intergranular Several small re- Large areas of

fracture gions severe IG cracking

3) Ductile fracture Large region Small region

4) Density of grain High Low

boundary strian

_ markings

5) Microvolds at Relatively few Many microvoids

internal sites showing agglomeration into a huge

void

6) Fracture surface Relatively clean be- Heavily oxidized.

cause little time is Oxide can someallowed for oxidation times mask the deof the surface tails of fracture surface topography.

The SEM photomicrographs illustrating the above features are presented in

Figures 11 (a) to 11 (d) . Multiple crack initiation sites and transition from Intergranular fracture to ductile fracture occurring in a high creep rate CP test are

shown in Fig. 11 (a) . Typical intergranular fracture and microvoid formation at

internal sites in a low creep rate CP test are illustrated in Fig. 11(b). These

tests were conducted on solid specimens of 316 SS at 1500°F. Similar photomicrographs for tests conducted on hollow specimens of 316 SS at 1300°F are

presented in Figs. 11(c) and 11 (d) . The features observed at 1300°F are

similar to those observed at 1500°F. Intergranular fracture with high strian

30

j ^.^t
E ss = 0.004024 in/in/min

N = 94

t = 3.5 hr

100 ,:m

i

E ss = 0.0000338 in/in/min

N = 46

IL f = 95.60 hr

I

CRIMP,,. r: ;;

OF POOR QUALITY

(a). Hiqh Creep rate test (h). Low Creep rate test

Fick. 11. Comparision of the Fracture Surface Topography

of a High Creep rate test and a Low Creep rate

test. 316 SS at 1500' F. 'c in = 2€,

31
'.:"t'N

•4r 1 ^..

' '• Microvoid formation

100 .

a

ORICINA,L P.- ,-

OF POOR QUALITY

(c). High Creep rate test (d). Low Creep rate test

j

Ductile fracture

r

rJ0

`

r^ 4

Y "

V

•

ss - 0.0006062 in/in/min = 0.0000430 in/in/min

ss

N = 69 Nf = v5

t = 10.1 hr t = 142.3 hr

Fiq. 11 (Continued) 316 SS at 1300° I', .1L in 21

32

I.^
density in a high creep rate constant creep strain CP test is visible in Fig.

11(c).

Macrophotographs of the metallographic sections of high creep rate and low

creep rate constant creep strain CP tests are illustrated in Figs. 12(a) and

12(b) . respectively. Two separate crack initiation sites on the surface of a high

creep rate CP test specimen are clearly visible in Fig. 12(a) . The material

between the two crack fronts fractured in a ductile manner. The intergranular

nature of fracture is distinctly visible in Fig. 12(b) . It appears that crack propagation occurs in a low creep rate CP test by means of linking the microvoids

and intergranular cracking formed ahead of crack tip within the bulk of the material. Thus the crack is propagated along a path that is already weakened by

microvoids and intergranular cracks. Multiple crack initiation sites developed at

the surface of a specimen in a high creep rate CP test and a huge void formed

during a low creep rate CP test can be seen in Figures 13(a) and 13(b)

respectively.

b) Oxide Formation

The formation of an oxide layer on the surface and within the crevice of the

crack can influence the crack growth rate and hence the cyclic life of a constant

creep strain CP test. During the rapid compressive loading in a CP cycle the

oxide gets "wedged" between the two lips of the crack. This can either sharpen

the crack tip to a greater extent or possibly propayste the crack during compression • if sufficiently thick oxide layer is available. A schematic of the oxide

wedging effect mechanism is shown in Fig. 14. Photomicrographs of the high

creep rate and low creep rate CP test specimens were obtained using an optical

microscope prior to etching to preserve the oxide layers. These photomicro-

.

33
(a). High Creep rate tt2st

Ess = 0.004024 in/in/min; N = 94; t = 3.5 hr-

(b). Low Creep rate test

SS = 0.0000338 in/in/min; N f = 46; t = 95.6 hr.

Fig. 12. Metallo.;.:aphs of specimens fatigued to failure

in CP t-,sts with varvinq exposure times.

316 SS at 1500° F. = 2i. in

IM

34
D ^ 1

P

the surface

a

50 um

Large void

\ 0 1

II

ORiGj; . ' "

OF POf.

(a). High Creep rate test

C ss = 0.004024 in/in/min; N f = 94; t, = 3.5 hr.

IL

50 um

(L), Low Creep rate test

Ess = 0.0000338 in/in/min; N = 46; t f = 95.6 hr.

Fig. 13. Typical Features of High Creep rate and Low

Creep rate CP tests with varyinq exposure

times. 316 SS at 1500° F. Lc. = 2%. in

35

►sy it
n

E (Strain)

eep Strain

teresis Loop

Oxide

Crack Opening

during Compression

Tensile Creep Compressive Plasticity

(slow) (fast)

Fig. 14. Oxide Wedge Effect.

36
graphs are illustrates in Figures 15(a) to 15(d) . The grey colored regions indicate the oxide layers. It is clear from these figures that the longer the failure

time (or lower the creep rate) , the greater the thickness of the oxide layer.

Also at high temperature (1500 0 F. Figs. 15(a) and 15(b)) , the oxide layer is

thicker than at a lower temperature ( 1300°F, Figs. 15(c) and 15(d) . An oxide

wedging effect is more likely to be observed when the oxide layer is thick than

when it is thin. In a slow creep rate CP test there is sufficient time for the oxide layer to form and develop into a thicker layer as compared to a high creep

rate CP test. Hence, oxide wedge effect is possibly one reason why a lower

cyclic life is observed in a low creep rate CP test as compared to a high creep

rate CP Zest.

c) MetallV roical Instabilities Mn Auster.iti Steel

AISI 316 stainless steel is an austenitic steel with chromium and nickel as

the mayor alloying elements. Unless the carbon content is very low (i.e. <

0. 02%) . the homogeneous structure of stainless steel ( after annealing between

1850 0 and 2050°F) is the result of quasi-equilibrium. Carbon is held in the

solution due to rapid cooling caused by quenching. When austenitic stainless

steels are reheated between 900° to 1700°F, the carbon in the supersaturated

solution is rejected and the resulting carbides alter the properties of steel. Sensitization to intergranular corrosion and changes in mechanical properties are two

direct consequences resulting from the precipitation of carbides. These carbides

are usually of the form M 23C 6 where M denotes any metal. M 23C 6 is usually

made up Of chromium carbide 'n which iron (or molybdenum) may substitute

partially for chromium.

37
(b) . Low Cre rate _es =

(a). High CreeF rate test

ss = 0.004024 in!ir ini- - \, _ p;; t. _ ---- --.

Fig. 13. ...._de Layer Fcr-at._-. :7

varyin g ex_ cs:._= __- E s. _ _ _ -= -- - ;

- = 21. in

38

KA
•

Y 

►►yy

• s

F—^

firm

OF " fi

{'W's L_DLD^D#.^ ; I s ice; Zi s 1[_. to

I

LOW Cry rate test

is _ [ _ DDDE4 3 st 1n 

'

air - r;i

3<
Statistically, the precipitation of chromium carbide is favored along the grain

boundaries, though precipitations can also occur at slip bands and around nonmetallic inclusions. The carbon atom being small diffuses more rapidly through

the austenitic crystal than chromium which is a bigger atom. As a result. during the process of precipitation, carbon atoms migrate to the grain boundary

from all parts of the crystal. whereas chromium is depleted from more localized

regions. near the grain boundary. thus creating an envelope of chromiumdepleted material in the vicinity of grain boundary. A schematic of this mechanism is illustrated in Fig. 16. Hence. the chromium-depleted grain boundaries

are susceptible to corrosion and fracture. In addition. the galvanic effect arising

between the precipitated chromium carbide particles and the austenite matrix can

accelerate the corrosion. At a given temperature the amount of chromium carbide increases with the time of exposure.

The metallographic sections of the specimens fatigued to failure in constant

creep strain CP tests were etched 1 and photographed using the scanning electron microscope. Figures 17(a) and (b) show the results of a high creep rate

CP test and low --reap rate CP test, respectively. at 1500 0 F. Figures 17(c)

and (d) show corresponding results for tests conducted at 1100^F. The short

time test (Fig. 17(a)) practically has no precipitation of chromium carbide along

the grain boundaries compared to the long time test (Fig. 17ib)) which shows

oxidized microvoids and separation of grain boundaries in regions far away from

1 Composition of the etchant used: (Proposed by Marble)

4 grams of copper sulphate

20 cc of hydrochloric acid

20 cc of water

40

Irl '
Annealed at 1850-205Cx° F + Hold Period

r7

Original Microstructure Reheated to 900-1700° F

o Chromium Carbide Precipitation

Chromium Depleted Zone

Fig. 16. Austenitic Stainless Steel (C > 0.020)

Schematic Illustration of Sensitization.

4,

1
ORIGINAL P,~CI t; 

(a). High Creep rate test P")R QUAL[n. LOW creep rate test 

Fig. 17. Cornparision of the Metallographic sections of 

spccirncnc fatigued to failure in CP 

tests wit11 varying exposure times. 316 SS at 

15GS0 F. :.. = 28. in 
it

the actual fracture surface. Comparing Figs. 17(c) and 17(d) . it can be seen

that more chromium carbide precipitation is present in the long time duration test

than in the short time duration test. In addition. Fig. 17(d) illustrates intergranular fracture that developed within the bulk volume of the material during a

long time duration test.

Since carbide precipitation makes the grain boundaries susceptible to fracture

(i. e. more brittle) and the amount of carbides precipitating increases with Vie

time at a given temperature. the grain boundaries are more vulnerable in long

time duration CP tests. This is one reason why lower cyclic life is observed in

long exposure time constant creep strain CP tests.

DISCUSSION

Time effects on Ncp have been treated in this report according to two types

of equations. Both of these equations are reproduced below for convenience.

The first type, namely the Steady State Creep Rate (SSCH) Modified CP life

equation,

Ncp = A IAE CP l Ess) ( l 1a)

is reminiscent of Coffin's Frequency Modified Life equation ( FML) . However, the

nature of the terms involved in this equation differ considerably from those in the

FML equation. As discussed more fully earlier in the report. the FML equation

reflects both a creep rate effect and a rheological effect wherein the ratio of CC

to PP strain changes as frequency is changed. Thus there would be an apparent "time" effect even if no metallurgical phenomena were introduced by

longer exposure, just because in the lower frequency tests a larger content of

43
aq

i

a

i

t_

m1

OF POOR QUALiT i

(c)_ High Creep rate test (d). Loh Creep rate test

mk^

..L. t I n 17. -in 0. 0, 000 i3 ir.;'ir.!^i-:

ss

r = 4 4

`'f = Y5

t = 142.3 hr

(ccnti_..:edl 326 -c at 1330° F._ = 21.

CC

M .

A4
. I ^6

the imposed strainrange becomes the CC type which is more damaging than the

PP type. Furthermore such -time" effects as are observed refer to effects on

the CC type of strainrange, and not on the CP type investigated in this study.

Extrapolations to lower creep rates by the FML equation would therefore not carry

the same fundamental implications regarding NcP as those determined from Eq.

(lla).

The second form of the equation, namely. the Failure Time (FT) Modified

CP life equation

NcP = B IAE CP 1 y f ff ) a (12a)

would seem to bear a closer relation to the Ductility Modified approach that has

been used in the past to correct N CP life for materials with ductilities in the extrapolation range which are different from those in the testing range. In fact, it

ductility can be expressed as a power law of rupture time, it is clear that the

two approaches could ideally produce identical results. Eq. (12a) would seem.

however, to be more direct. and probably more accurate for moderate extrapolations of rupture times. For very long extrapolations, the favor might revert to

the Ductility Modified equation approach, since actual ductilities for very long

times ( say 105 hrs.) might be available from creep-rupture tests while Eq.

( 12a) reflects ductility variation in only the experimental range for the cycling

tests. Thus, if a material develops a metallurgical instability (say the precipitation of a sigma phase) after 10.000 hrs. , the creep rupture tests, although they

are static, are more likely to reveal this development more accurately than a

shorter time fatigue test. Since static creep-rupture tests on many materials are

more plentiful than creep-fatigue tests, use of ductility information revealed by

45
these tests should not be overlooked, even tnough equations of the form ( 12a)

may give more accurate results in the creep-fatigue experimental range. For the

tests of this investigation, for example. Eq. (12a) gave correlations within a factor of 1.5 on life in the experimental range while the Ductility-Modified approach

gave results within a factor of 2.0. However, if long-time ductility in creeprupture tests are available their implications for long-time extrapolation of creepfatigue tests should not be overlooked. It should also be recognized, of course.

that if ductility degrades in an abrupt manner only after long time exposure, the

creep-fatigue analysis must proceed on a cycle-by-cycle basis reflecting in each

applied cycle only the damage that is developed for a cycle within the material at

its current ductility. This subject has been discussed in Ref. (6. 19) .

Although both forms of the equations (1 la) and (12a) give approximately the

same degree of accuracy in the experimental range used in this investigation, it

should not be inferred. of course. that both forms are identical. Obviously,

since the exponents on AECP are different, computed lives by each of the two

equations must be at least slightly different even if a relation between rupture

time and creep rate exists. Thus, although it is possible that the IESS in

Eq. (1 la) , and the Itf ) b in Eq. ( 12a) are inter-related and yield the same

mathematical information, the fact that a is not equal to 'Y indicates that the two

equations will not always yield the same life value. Which type of equation is

more useful for extrapolation requires further study.

It should also be pointed out that the time (or creep-rate) effect on the CP

life relation was obtained by assuming that the PP life relation was not timedependent. When only PP cycles are applied a time-dependency need not be

considered, since in principle a very large number of cycles can be applied in a

46

^4,1
.._...`

Fi

M,

very short time. However, when, in effect, the PP cycles are applied concurrently with the CP cycles, the PP cycles are also applied as the material is

degrading while the material interacts with the environment and degrades metallurgically. Thus it is possible that some consideration should be given to NPP

degradation with time. which might change the result of these tests to some extent.

In this investigation we have considered only the CP type of strainrange. It

is clear that for complete SRP analyses involving other types of strainranges,

similar studies are required for PC. CC and even PP, as mentioned above. For

evaluations of time effects on PC lives, the approach used in this study can be

used in a similar manner, but for CC evaluations there are two independent variables -- the creep rate in tension and the creep rate in compression. The time

effects on CC strainranges will therefore require additional consideration in order

to minimize the extent of the testing program involved.

A final point that must be considered for future programs on any of the types

of strainranges associated with the SRP framework. When an imposed loop contains more than one strainrange. the experimental information obtained provides

information only on life for each type of strainrange for a magnitude equal to the

total strainrange of the loop. Thus, for example, if the total *rainrange is 1%

and consists of a CP strainrange of 0.5% and PP strainrange of 0.5%, the test

involves information on NpP and Ncp for AE PP = 1% and AEcp = 1%. If the

test were changed so that the imposed 1% total strainrange consisted of 0. 75%

CP and 0.25% PP, the information involved in the test still only involves NpP

and NCp for a strainrange of 1%. This is a peculiarity of the Interaction Damage Rule. Thus, to get information on Ncp at a strainrange of 2%, the loop

used must have a total strainrange of 2%. and it doesn't matter whether 0.5%

47
A"*

or 1%. or 1.5% of this loop consists of CP strainrange. Obviously, however,

the larger the fraction of the total strainrange that is imposed as CP, the more

accurate will be the information on the life Ncp at the strainrange of 2%. In

the tests conducted in this program the PP component was included for convenience of programming to maintain constant total strainranges even though some

variation in CP strainrange inevitably occurred. However, it would seem that in

future tests the control system should be improved to minimize the amount of PP

needed, and to keep the CP (or other components, when they are studied) at

the largest fraction of the total strainrange practicable.

SUMMARY AND CONCLUDING REMARKS

The effect of creep rate (or exposure time) within the CP strainrange (or

waveform) was investigated by conducting a series of CP tests with varying creep

rates (or exposure times) on 316 SS at 1300°F and 1500°F. A reduction in

NcP lives was observed with a reduction in the creep rate (or with an increase

in the exposure time) .

The reasons for the reduction of cyclic life as creep rate decreases are

summarized below:

1. In the case of a low creep rate test, cracks propagate by linking the

microvoids and minute cracks caused by grain boundary separation, i.e. , they

propagate along a path that is already weakened by microvoids and intergranular

cracks. In a high creep rate test since sufficient time is not allowed for microvoid formation, crack propagation requires physical separation of grain boundaries. Hence the crack growth rate IdN l in the case of low creep rate test

is likely to be much higher thar, the one in the high creep rate test.

49

^l^
2. Oxide layers within the crack crevices of a specimen can accelerate the

crack growth rate due to an oxide wedge effect. A low creep rate test allows

sufficient time for the build-up of oxide layers and hence the wedge effect can

reduce the cyclic life of a low creep rate test more than a high creep rate test.

3. The sensitization of austenitic stainless steel, due to the precipitation of

chromium carbide along the grain boundaries, can mat-R the steel more susceptible to intergranular corrosion. Hence a long time duration test ( low creep

rate) is more damaging than a short time duration test ( high creep rate) .

The reduction in cyclic life with a reduction in creep rate is a combined effect of micromechanistic darnages occurring in the material due to low creep

rates and due to environmental effets such as oxidation, corrosion, etc. In order to separate the damage associated with the material's rheological behavior

from the damage caused to the material by the environment, similar tests should

be conducted in vacuum or an inert atmosphere.

The Ductility-Normalized SRP life relationships can also be used to account

for the reduction in cyclic life with an increase in the failure time but not with

the same accuracy as was obtained with the new relations. The predictions of

DN-SRP life relationships were generally within a factor of 2. When no cyclic

creep fatigue data are available DN-SRP relations satisfactorily predict lives.

The conventional Strainrange Partitioning method predicted the lives within a

factor of 2. However, conventional SRP does not account for frequency effects

within a given type of strainrange. The Steady State Creep Rate (SSCR) Modified CP life relationship and the Failure Time (FT) Modified CP life relationship

predicted the lives within a factor of 1.5. Thus life predictions can be improved

by accounting for the effect of frequency and waveform in a distinct manner. It

is also necessary to account for exposure time (or creep rate) when the creep

49
fatigue data generated at short times are being extrapolated to longer times.

As Illustrated In the discussion section, there Is a difference

between the SSCR Modified CP life relationship and the FT Modified CP life relationship. The question as to which one of these two equations is more appropriate depends upon the circumstances. In the future more experiments

should be conducted on a wide spectrum of materials to resolve this issue. The

present work provides a good format for such future investigations.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial support (Grant Number:

NAG3-337, Dr. G. R. Halford, Grant Monitor) provided by NASA-Lewis Research

Center, Cleveland. Ohio.

50

¢-•
REFERENCES

1. Manson, S.S. , G. R. Halford and M. H. Hirschberg: "Creep-fatigue

analysis by strain-range partitioning, " NASA TM X-67838, Technical paper

presented at Pressure Vessels and Piping Conference sponsored by the

American Society of Mechanical Engineers. San Francisco. California. May

10-12, 1971.

2. Halford, G. R. , J. F. Saltsman and M. H. Hirschberg: 'Ductility-Normalized

Strainrange Partitioning Life Relations forCreep-Fatigue Life Predictions" -

NASA TM-73737, Technical paper presented at the Conference on Environmental Effects and Degradation of Engineering Materials, sponsored by the

Virginia Polytechnic Institute. Blacksburg, Virginia. October 10-12, 1977.

3. Kalluri, S.. "The effect of creep rate on Strainrange Partitioning life relationships. " M. S. Thesis. Department of Mechanical and Aerospace Engineering, Case Western Reserve University, January. 1984.

4. Manson, S. S. , G. R. Halford and A. J. Nachtigall: 'Separation of the

strain components for use in strainrange partitioning." NASA TM X-71737,

Technical paper presented at Pressure Vessels and Piping Conference,

sponsored by The American Society of Mechanical Engineers. San Francisco. California. June 23-27, 1975.

5. Hirschberg, M. H.: "A Low Cycle Fatigue Testing Facility, " Manual on low

cycle fatigue testing, ASTM STP 465, American Society for Testing Materials. 1969. pp 67-86.

6. Coffin, L. F. Jr. , A. E. Carden, S. S. Manson, L. K. Severud and W L.

Greenstreet: "Time-Dependent Fatigue of Structural Alloys, A General Assessment" ( 1975) , prepared by the Oakridqe National Laboratory. Oakridge. Tennessee, January 1977, pp 37-332.

7. Manson, S. S.: 'The Challenge to Unify Treatment of High Temperature

Fatigue - A Partisan Proposal Based on Strainrange Partitioning. " Fatigue

at Elevated Temperatures. ASTM STP 520, American Society for Testing

and Materials. 1973. pp 744-782.

8. Manson, S. S. and G. R. Halford: "Complexities of High Temperature Metal

Fatigue - Some Steps Toward Understanding. " Technical paper presented

at The Twenty-fifth Annual Israeli Conference on Aeronautics and Astronautics sponsored by the University of Haifa. Haifa. Israel. February 23-25,

1983. NASA TM 83507.

9. Halford, G. R.. A. J. Nachtigall: 'The Strainrange Partitioning Behavior of

an Advanced Gas Turbine Disk Alloy, AF2-1DA" AIAA/SAE/ASME 15th Joint

Propulsion Conference. June 18-20, 1979, Las Vegas, Nevada. pp. 4-8.

10. Manson. S. S.. G. R. Halford and R. E. Oldrieve: 'Relation of Cyclic Loading Pattern to Microstructural Fracture in Creep-Fatigue.' Proceedings, The

L

^s f . ;.:•. . r

51
Second International Conference on Fatigue and Fatigue Thresholds. Birmingham. 1984. C. J. Beevers Ed.. Engineering Materials Advisory Services

Ltd.. West Midlands, U-K, 1984,

11. Parr. J.G. and A. Hanson. 'An Introduction to Stainless Steel." American

Society for Metals. 1965. pp. 52-56.

12. Colombier. L. and J. Hockmann: "Stainless and Heat Resisting Steels.'

Edward Arnold ( publishers) Ltd.. 1967. pp. 84-93.

13, Peckner. D. and I.M. Bernstein: "Handbook of Stainless Steels.'

McGraw-Hill Rook Company. 1977, pp. 4-35 to 4-52.

14. Williams. R. S. and V. O. Homeberg: "Principles of Metallography. " Third

edition. McGraw-Hill Book Company. Inc.

15. Oldrieve, R. E.: "Fractographic Evaluation of Creep Effects on Strain Controlled Fatigue Cracking of AISi 304 LC and 316 Stainless Steel.' NASA

TM-78913, Lewis Research Center. Cleveland. Ohio. June 1978.

16. Rostoker. W. and J. R. Dvorak: "Interpretation of Metallographic Structures. " Second edition. 1977. Academic Press Inc.. pp. 66-74.

17. "MTS Basic RT-11 Users Guide.' MTS Systems Corporation. November

1976.

18. 'MTS Basic Assembly Language Routines Program Manual.' MTS System!•

Corporation, July 1977.

19. S. S. Manson and R. Zab: "Treatment of Low Strains and Long Hold

Times in High Temperature Metal Fatigue by Strainrange Part:iioning. "

ORNL/Sub-3988/1 August, 1977.

52
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57
CONSTANT CREEP STRAIN"CP" TEST INPUT DATA FOR CONCP.RAS

1. Specimen Identification Number : K1$

2. Numerical value of the Percentage

of the Load Scale : S1

J. Numerical Value of the Percentage

of the Strain Scale . S2

4. Tensile Creep Load in Pounds . PO

S. Diametral Inelastic Displacement

"age . DO

6. Di wetral Displacement Range

Corresponding to the Amount of

Creep to be Introduced . DS

7. First Cycle Tensile Diametral

Displacement Limit : D1

g . Subsequent Tensile Diametral

Displacement Limit • D3

9. Compressive Diametral

Displacement Limit D4

10.lnteger representing the C-irrent

Hour, based on s 24-hour Day Ul

ll.lnteger representing the

Current Minute V1

12.1ateger representing the

Current Second Iii

13.Integer representing the

Current Month Y1

14.Inceger representing the

Current Day of the Month YI

1S.Integer representing the

Current Year 21

Sample data input sheet for CONCP.BAS program.

58
8 = IogNcp -IogA -alogA Ecp-,Slog Ess (B-3)

C^1

APPENDIX B

Multiple Regression Analysis

Let there be n experimental data points ( n > 3) that are available for the

evaluation of the Steady State Creep Rate (SSCR) Modified CP life relationship.

Each of these data points contains (a) the generic CP cyclic life Ncp . (b) the

inelastic strainrange. Ac CPand (c) the stew Jy state creep rate. Ess

The SSCR Modified CP life relationship is of the form

Ncp = A (A Ecp a t Ess rB (8-1)

The constants A , a and B are obtained from a multiple regression analysis.

Taking logarithms (to base 10) on both sides.

IogNcp = IogA + a log A EcP + ,Blog Ess (8-2)

Error occurring in cyclic life NCp prediction. due to regression analysis.

Squaring on both sides.

82 = IogNcp -IogA -alogA EcP-,Slog Ess ] 2

Summing from i = 1 to n to add all the squares of the errors occurring at

each data point ( i. e. i = 1 , ... , n) , total of the squares of error

(B-4)

n n

82 = 82 = log (NCp i - IogA -alog (AECp ! - Blog I Ess ^ i ^ 2 1=1 i=1 l

t

59

r'_
To minimize the error in Ncp .0 2 should be minimized with respect to A . a and

0.

aA (62 = 0

da (152) = 0 (B-5)

aQ 

( 6

2) = 0

Substituting (B-4) into Eqs. (B-5) . and then interchanging the summation

and differentiation operations, the following equations are obtained.

n

i1 log ( NcP ) i

- IogA-alog AE Cp )

i

 - ,Slog ^ESSJi}- l- A2—log 1U^ =I 0

(B-6)

n ( 1r 1

i

ll J ^ IOg (Ncp ) i -IogA -alog I cp ) i- ^ IOg I ESS) I- (-210g I cP)) _ ()

i 

n

t i log (l(NcP ) i -IogA -alog (AEcP ) i -Qlog I Ess ) i }'^ -21og E ss) 1 J = 0

Since A * 0, and log1 0 and 2 are finite constants they can be cancelled in

Eqs. (B-6) . After some algebraic manipulation Eqs. (B-6) can be arranged in

the following matrix form:

Using the following notation,

60
a ll = n

n

a 12 - 821 iEl log I AEcp ), n

813 = 831 i ^1 log I 

Ess J i

n

2

a 22 

= Ilog (ac, 1i }

 l

J

n

a23 -

a 32 log 

E ss i t °g 

^ AECP i

n

2

a33 = E 1 log Ess }

i-1 l

x

l = log A

x2 = a C ,

x3 = Q

n

8 1 

= log (Nop 1 i

i=1

l

1

6

61 t
n

@ 2 = Elog 

INCP J i R log ( AccP l i 1=1

n

B 3 = E log (NCP, i " log l Ess i i=1 l I

a ll 8 12 8 13 X1 81

a 21 8 22 8 23 x2 82

a 31 8 32 a33 Ix 3 IB 3

(6-7)

Constants IogA , o and a are obtained by solving the system of Eqs. (B-7)

simultaneously. For Failure Time (FT) Modified CP life relationship, Steady state

creep rate. E ss should be replaced by time to failure t, in the above analysis.

62

l
1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.

NASA CR- 174946

4. Title and Subtitle 5. Report Date

Time Dependency of Strainrange Partitioning Life August 1984

Relationships 6. Performing Organization Code

7. Authors) 8. Performing Organization Report No.

Sreeramesh Kalluri and S.S. Manson None

10. Work Unit No.

9. Performing Organization Name and Address

1. Contractor Grant No.

NAG 3-337

Case Western Reserve University

Cleveland, Ohio 44106

13. Type of Report and Period Covered

12. Contractor Report Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, D.C. 20546

14. Sponsoring Agency Code

533-13-01

15. Supplementary Notes

Final report. Project Manager, Gary R. Halford, Structures Division, NASA Lewis

Research Center, Cleveland, Ohio 44135.

16. Abstract

The effect of exposure time (or creep rate) on the CP life relationship is established by conducting isothermal CP tests at varying exposure times on 316 SS at

1300 and 1500 °F. A reduction in the CP cycle life is observed with an increase

in the exposure time of the CP test at a given inelastic strainrange. This phenomenon is characterized by modifying the Manson-Coffin type of CP relationship.

Two new life relationships, (i) the Steady State Creep Rate (SSCR) Modified CP

life relationship, and (ii) the Failure Time (FT) Modified CP li f c relationship,

are developed in this report. They account for the effect of creep ra g a and

exposure time within the CP type of waveform. The reduction in CP cyclic life

in the long exposure time tests is attributed to oxidation and the precipitation

of carbides along the grain boundaries.

17. Key Words (Suggested by Author(s)) 18. Distribution Statement

Fatigue (metal); Creep-fatigue:, Strain- Unclassified - unlimited

range partitioning; Life prediction; STAR Category 39

Ductility; Strain cycling

I

19. Security classic (of this report) 20. Security Claself. (of this page) 21. No, of pages 22. Price'

Unclassified Unclassified

. For sale by the National Technical Information Service, Springfield, Virginia 22161

_,J